Class 10: Channels of Distribution and Double Marginalization
Textbook reading: Kreps, Chapter 9. Read all of it, but treat the algebra in section 9.1 as something to check rather than reproduce: every MR = MC step in the chapter is a straight-line demand, so Lab 4’s halfway rule (the best price sits halfway between marginal cost and the price at which demand hits zero) gets every number. Skip the derivative on page 207. A warning about Table 9.1 on page 210: several of its entries do not match the text’s own formulas.
Key Ideas
A chain of markups
- Most goods travel manufacturer → retailer → customer
- Each link has market power and sets MR = MC
- Each link’s marginal cost is the previous link’s price, which already contains a markup
- Double marginalization: the good is marked up, then marked up again
- Why Tesla sells direct, and why car dealers lobby state legislatures to stop it
Solving the chain
- Backward induction: solve the retailer first, then the manufacturer
- Compared with one integrated firm: fewer units, a higher retail price, and lower total profit
Why retailers exist anyway
- Retailers are often better at retailing: closer to customers, cheaper inventory, better at price discrimination
- The real comparison is double marginalization against the retailer’s cost advantage
Fixing the chain
- Two-part tariff: wholesale price equal to marginal cost, plus an up-front franchise fee
- The per-unit price sets the size of the pie; the fee only slices it
- Resale price maintenance: the manufacturer fixes the retail price
- Vertical integration: the manufacturer buys the retailer
Problems of the Day
Q28: The Second Hundred
Priya builds e-bikes for $200 each and sells them through Marco’s shop at $350 apiece. Marco has no other costs and sets the retail price; his monthly demand is in the table. For two years he has charged $700.
| Retail price | $500 | $600 | $700 | $800 | $900 |
|---|---|---|---|---|---|
| Bikes a month | 10 | 8 | 6 | 4 | 2 |
Dev, Priya’s sales manager, wants the wholesale price raised to $450: “Marco will keep his $700 and we pocket $100 on each of six bikes.” Marco warns that any increase goes straight onto his sticker. Priya tries $450, and Dev turns out to be exactly right.
- Explain why, when Priya raises the wholesale price from $350 to $450, it’s Marco’s best response to keep the retail price at $700 instead of raising it as well.
- What will happen if Priya raises the wholesale price to $550?
Q29: Rent for a Bike Shop
Priya now charges Marco $450, and each of them clears $1,500 a month. She offers a new deal: bikes at her cost of $200, plus a flat $1,650 a month for the right to sell them. Demand is as in Q28.
Marco’s bookkeeper runs the numbers: “Six bikes at $500 over cost is $3,000, less $1,650 is $1,350. She is asking you to pay $150 a month for the privilege of working for her.” Priya insists the deal makes both of them richer.
How much does signing gain or cost Marco?
Q30: Cutting Out the Middleman
Lena, on Priya’s board, objects to the deal in Q29: “Why pay Marco anything? Open a web store and sell direct. We keep the whole $3,200, and customers get their bikes cheaper with no middleman taking a cut.” Operations estimates that shipping, returns and service would cost Priya an extra $150 a bike; Marco’s shop does all that at no cost to her. Demand is as in Q28.
What does the web store do to the price a customer pays?
Answers
- Q28. Why $700 survives the raise. Marco keeps whatever is left after paying Priya, so he compares his own margin row by row. At $350 wholesale his profit at $600, $700 and $800 is $2,000, $2,100 and $1,800: $700 wins. At $450 the same three stickers pay $1,200, $1,500 and $1,400: $700 still wins. Moving the sticker to $800 would gain him $100 on the four bikes he keeps but give up a $250 margin on each of the two he loses, and $400 is less than $500. So Marco swallows the raise, and Priya pockets $100 on six bikes, $1,500 instead of $900, exactly as Dev said. At $550. Now Marco’s margin at $700 is only $150, so the two bikes lost by moving to $800 cost him $300 against the $400 gained, and the move pays: his profit at $700, $800 and $900 is $900, $1,000 and $700. He charges $800 and sells four, and Priya earns $350 × 4 = $1,400, down $100 from $1,500. The first raise only moved margin from Marco’s pocket to Priya’s because $700 stayed his best sticker; the second thinned his margin enough that giving up bikes stopped hurting him, and the two lost bikes cost Priya more than her fatter margin earns.
- Q29. Marco’s best sticker at $200. His profit at $500, $600, $700 and $800 is $3,000, $3,200, $3,000 and $2,400, so he drops the sticker to $600 and sells eight. Gross $3,200, less the $1,650 fee, leaves $1,550. He clears $1,500 today, so signing gains him $50. Where the bookkeeper went wrong. Her $1,350 assumes Marco keeps charging $700 after his cost falls from $450 to $200. At $700 he would indeed earn $3,000 less $1,650 and lose $150, but $700 is no longer his best sticker. Priya. She collects $1,650 and nothing per bike, up $150 from $1,500. Both are richer because at $200 a bike Marco faces the same cost Priya does, so the sticker that is best for him is the one that is best for the pair, and the pie grows from $3,000 to $3,200 before the fee divides it.
- Q30. The web store’s price. Every bike now costs Priya $350 to make and deliver. Her profit at $600, $700 and $800 is $2,000, $2,100 and $1,800, so she charges $700 and sells six. Under the Q29 deal Marco charged $600, so the web store raises the price a customer pays by $100, and two customers a month stop buying. Why Lena is half right. She earns $2,100 direct against $1,650 from the deal, so cutting out Marco does add $450 to Priya’s profit. But the “middleman’s cut” was already gone: the Q29 deal sells Marco bikes at cost, so the only markup customers pay is the one that is best for the pair. The web store replaces a cut of zero with $150 a bike of Priya’s own retailing cost, and the sticker rises to cover it.